We deal with an initial boundary value problem of nonhomogeneous Boussinesq equations for magnetohydrodynamics convection in two-dimensional domains. We prove that there is a unique global strong solution. Moreover, we show that the temperature converges exponentially to zero in H1 as time goes to infinity. In particular, the initial data can be arbitrarily large and vacuum is allowed. Our analysis relies on energy method and a lemma of Desjardins (Arch. Rational Mech. Anal. 137:135–158, 1997).

中文翻译：

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磁流体动力学对流非齐次 Boussinesq 方程强解的全局适定性和衰减估计

我们处理二维域中磁流体动力学对流的非齐次 Boussinesq 方程的初始边值问题。我们证明了存在一个独特的全局强解。此外，我们证明了温度在H1随着时间的流逝。特别是，初始数据可以任意大，并且允许真空。我们的分析依赖于能量方法和 Desjardins 的引理（Arch. Rational Mech. Anal. 137:135–158, 1997）。